For this distance, closedness and convexity of \(f\) 
guarantee that the proximal operator is well defined.
The questions of existence and uniqueness are more complicated for
general Bregman distances.
There are no simple general conditions that guarantee that for
every \(a\)  and every \(y \in \mathop {\bf int}(\mathop {\bf dom}\phi )\) 
the generalized proximal operator (REF ) is uniquely
defined and in \(\mathop {\bf int}(\mathop {\bf dom}\phi )\) .
Some sufficient conditions are provided
(see, for example, [1]},
[2]}),
but they may be quite restrictive or difficult to verify in practice.
In applications, however, the Bregman proximal operator is used with
specific combinations of \(f\)  and \(\phi \) , for which the minimization problem
in (REF ) is particularly easy to solve.
In those applications, existence and uniqueness of the solution follow
directly from the closed-form solution or availability
of a fast algorithm to compute it.
A typical example will be provided in Section .
